4 papers
Sharp homogeneous Gagliardo--Nirenberg inequalities and normalized solutions for generalized stationary MMT equations
Amin Esfahani, Mukhtar Karazym
We prove the existence of optimizers for a class of homogeneous Gagliardo-Nirenberg inequalities of the form $$ \|D^{s}ϕ\|_{L^q} \leq C \|D^{s_1}ϕ\|_{L^p}^{1-θ} \|D^{s_2}ϕ\|_{L^2}^…
Traveling Waves for Nonlocal Derivative Nonlinear Schrödinger Equations: A Variational Characterization
Amin Esfahani, Adilbek Kairzhan, Mukhtar Karazym
We establish several existence results for traveling-wave solutions of the nonlocal derivative nonlinear Schrödinger equation with general coefficients by variational methods. We s…
The Cauchy problem for the nonlinear Schrödinger equation with a convolution potential
Amin Esfahani, Achenef Tesfahun
This paper investigates the nonlinear Schrödinger equation with a singular convolution potential. It demonstrates the local well-posedness of this equation in a modified Sobolev sp…
On the Kadomtsev-Petviashvili equation with double-power nonlinearities
Amin Esfahani, Steven Levandosky, Gulcin M. Muslu
In this paper, we delve into the study of the generalized KP equation, which incorporates double-power nonlinearities. Our investigation covers various aspects, including the exist…